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Eventdriven simulations of nonlinear integrateandfire neurons
"... Eventdriven strategies have been used to simulate exactly spiking neural networks. Previous works are limited to linear integrateandfire neurons. In this note we extend event driven schemes to a class of nonlinear integrateandfire models. Results are presented for the quadratic integrateandfir ..."
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Eventdriven strategies have been used to simulate exactly spiking neural networks. Previous works are limited to linear integrateandfire neurons. In this note we extend event driven schemes to a class of nonlinear integrateandfire models. Results are presented for the quadratic integrateandfire model with instantaneous or exponential synaptic currents. Extensions to conductancebased currents and exponential integrateandfire neurons are discussed. 1
Voltagestepping schemes for the simulation of spiking neural networks, in "Journal of Computational Neuroscience
 n o 3. Publications of the year Articles in International PeerReviewed Journals BIPOP 15
"... The numerical simulation of spiking neural networks requires particular attention. On the one hand, timestepping methods are generic but they are prone to numerical errors and need specific treatments to deal with the discontinuities of integrateandfire models. On the other hand, eventdriven met ..."
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The numerical simulation of spiking neural networks requires particular attention. On the one hand, timestepping methods are generic but they are prone to numerical errors and need specific treatments to deal with the discontinuities of integrateandfire models. On the other hand, eventdriven methods are more precise but they are restricted to a limited class of neuron models. We present here a voltagestepping scheme that combines the advantages of these two approaches and consists of a discretization of the voltage statespace. The numerical simulation is reduced to a local eventdriven method that induces an implicit activitydependent time discretization (timesteps automatically increase when the neuron is slowly varying). We show analytically that such a scheme leads to a highorder algorithm so that it accurately approximates the neuronal dynamics. The voltagestepping method is generic and can be used to simulate any kind of neuron models. We illustrate it on nonlinear integrateandfire models and show that it outperforms timestepping schemes of RungeKutta type in terms of simulation time and accuracy.
Introducing numerical bounds to improve eventbased neural network simulation, 2009, http://hal.inria.fr/inria00382534/en/, RR6924, Rapport de recherche
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Covert attention with a spiking neural network
 Int. Conf. on Computer Vision Systems (ICVS), volume 5008 of Lecture Notes in Computer Science
, 2008
"... Abstract. We propose an implementation of covert attention mechanisms with spiking neurons. Spiking neural models describe the activity of a neuron with precise spiketiming rather than firing rate. We investigate the interests offered by such a temporal code for lowlevel vision and early attenti ..."
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Abstract. We propose an implementation of covert attention mechanisms with spiking neurons. Spiking neural models describe the activity of a neuron with precise spiketiming rather than firing rate. We investigate the interests offered by such a temporal code for lowlevel vision and early attentional process. This paper describes a spiking neural network which achieves saliency extraction and stable attentional focus of a moving stimulus. Experimental results obtained using real visual scene illustrate the robustness and the quickness of this approach. Key words: spiking neurons, precise spiketiming, covert attention, saliency 1
Visual focus with spiking neurons
"... Abstract. Attentional focusing can be implemented with a neural field [1], which uses a discharge rate code. As an alternative, we propose in the present work an implementation based on spiking neurons. Such implementation will allow to investigate the possible contribution of a spike time based cod ..."
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Abstract. Attentional focusing can be implemented with a neural field [1], which uses a discharge rate code. As an alternative, we propose in the present work an implementation based on spiking neurons. Such implementation will allow to investigate the possible contribution of a spike time based code with a network of leaky integrateandfire neurons. The network is able to detect and to focus on a stimulus even in the presence of distractors. Experimental data show that this behavior is very robust to noise. This process implements an early visual attention mechanism. 1
LETTER Communicated by Hans Plesser A Generalized Linear IntegrateandFire Neural Model Produces Diverse Spiking Behaviors
"... For simulations of neural networks, there is a tradeoff between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrateandfire model that produces a wide variety of spiking behavi ..."
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For simulations of neural networks, there is a tradeoff between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrateandfire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firinginduced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model’s rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This singleneuron model can be implemented using algorithms similar to the standard integrateandfire model. It is a natural match with eventdriven algorithms for which the firing times are obtained as a solution of a polynomial equation. 1
A short course in mathematical neuroscience
, 2015
"... This book has two main aims: to teach how mathematical models that illuminate some parts of neuroscience can be constructed, primarily by describing both “classic ” and more recent examples; and to explain mathematical methods by which these models can be analyzed, thus yielding predictions and exp ..."
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This book has two main aims: to teach how mathematical models that illuminate some parts of neuroscience can be constructed, primarily by describing both “classic ” and more recent examples; and to explain mathematical methods by which these models can be analyzed, thus yielding predictions and explanations that can be brought to bear on experimental data. Theory is becoming increasingly important in neuroscience [1], not least because recent developments in optogenetics, imaging and other experimental methods are creating very big data. Computational approaches already play a substantial rôle [59, 60], and modelers are becoming more ambitious: the European Blue Brain project [184]
On the Performance of Voltage Stepping for the Simulation of Adaptive, Nonlinear IntegrateandFire Neuronal Networks
"... In traditional eventdriven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrateandfire model. In a recent paper, Zheng, Tonnelier, and Martine ..."
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In traditional eventdriven strategies, spike timings are analytically given or calculated with arbitrary precision (up to machine precision). Exact computation is possible only for simplified neuron models, mainly the leaky integrateandfire model. In a recent paper, Zheng, Tonnelier, and Martinez (2009) introduced an approximate eventdriven strategy, named voltage stepping, that allows the generic simulation of nonlinear spiking neurons. Promising results were achieved in the simulation of single quadratic integrateandfire neurons. Here, we assess the performance of voltage stepping in network simulations by considering more complex neurons (quadratic integrateandfire neurons with adaptation) coupled with multiple synapses. To handle the discrete nature of synaptic interactions, we recast voltage stepping in a general framework, the discrete event system specification. The efficiency of the method is assessed through simulations and comparisons with a modified timestepping scheme of the RungeKutta type. We demonstrated numerically that the original order of voltage stepping is preserved when simulating connected spiking neurons, independent of the network activity and connectivity.